With an average acceleration of -.56 m/s2, how long will it take a cyclist to bring a bicycle with an initial speed of 13.3 m/s to a complete stop?
t = (Vf - Vo) / a,
t = (0 - 13.3) / -0.56 = 23.75s.
To solve this problem, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the cyclist comes to a complete stop)
u = initial velocity (13.3 m/s)
a = average acceleration (-0.56 m/s^2)
s = displacement (unknown)
Rearranging the equation, we get:
0 = (13.3 m/s)^2 + 2(-0.56 m/s^2)s
Simplifying the equation further:
0 = 176.89 m^2/s^2 - 1.12 m/s^2s
Rearranging to solve for s:
1.12 m/s^2s = 176.89 m^2/s^2
s = 176.89 m^2/s^2 / 1.12 m/s^2
s ≈ 157.92 m
We know that displacement (s) is equal to the initial velocity (u) multiplied by the time (t), plus half the average acceleration (a) multiplied by the square of the time.
s = ut + 0.5at^2
Rearranging the equation, we have:
157.92 m = 13.3 m/s * t + 0.5 (-0.56 m/s^2) * t^2
157.92 m = 13.3t - 0.28t^2
Rearranging and simplifying, we have a quadratic equation:
0.28t^2 - 13.3t + 157.92 = 0
We can solve this equation using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
Where:
a = 0.28
b = -13.3
c = 157.92
t = (-(-13.3) ± √((-13.3)^2 - 4(0.28)(157.92))) / 2(0.28)
Simplifying further:
t = (13.3 ± √(176.89 - 177.126)) / 0.56
t = (13.3 ± √(-0.236)) / 0.56
Since the term inside the square root is negative, it means there are no real solutions. This indicates that the cyclist will not be able to come to a complete stop with an average acceleration of -0.56 m/s^2.
Therefore, the time it takes for the cyclist to bring the bicycle to a complete stop cannot be determined with the given parameters.
To determine the time it takes for the cyclist to bring the bicycle to a complete stop, you can use the formula for acceleration:
Final velocity (vf) = initial velocity (vi) + acceleration (a) x time (t)
In this case, the final velocity will be 0 because the bicycle needs to come to a complete stop. The initial velocity (vi) is given as 13.3 m/s, and the acceleration (a) is -0.56 m/s² (negative because it acts in the opposite direction to the initial velocity).
Setting vf to 0, vi to 13.3 m/s, and a to -0.56 m/s², we can solve for t:
0 = 13.3 m/s + (-0.56 m/s²) * t
Rearranging the equation to isolate t:
-13.3 m/s = -0.56 m/s² * t
Dividing both sides of the equation by -0.56 m/s²:
t = (-13.3 m/s) / (-0.56 m/s²)
t ≈ 23.75 seconds
Therefore, it will take approximately 23.75 seconds for the cyclist to bring the bicycle to a complete stop.